Calculus II – Workshop #29 - Edubirdie

University:
San Diego State University
Course:
MATH 151 | Calculus II
Academic year:

2023
Views:

40

Pages:

1
Author:

zufriedendyu

Workshop #29 1. Consider the region bounded by the graph of f (x) = is then rotated about the y-axis. √ 1 − x, the x-axis, and the y-axis. This region (a) Find the volume of the resulting solid using the disk/washer method. (b) Find the volume of the resulting solid using the shell method. 2. Integrate the following. Z √ (a) x ln x dx Z sin x dx 1 + cos x Z arctan x dx 1 + x2 (b) (c) Z 1 x2 ex dx (d) 0 Z 4 (e) 1 3 0 (4 − x) 2 dx 3. Determine whether the following series are absolutely convergent, conditionally convergent, or divergent. (a) (b) (c) ∞ X (−1)n n2n n=1 ∞ X 3n+1 (−1)n (n2 + 5n3 ) √ n + 9n4 + 4n2 n=1 ∞ X (−1)n n=1 cos n

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